F. A. Kulacki

Natural convection in porous media

This book presents the papers given at a conference on free convection in porous materials. Topics considered at the conference included heat transfer, nonlinear temperature profiles and magnetic fields, boundary conditions, concentrated heat sources in stratified porous media, free convective flow in a cavity, heat flux, laminar mixed convection flow, and the onset of convection in a porous medium with internal heat generation and downward flow.

Coupled heat and mass transfer by natural convection from vertical surfaces in porous media

Abstract Similarity solutions for buoyancy induced heat and mass transfer from a vertical plate embedded in a saturated porous medium are reported for (1) constant wall temperature and concentration, (2) constant wall heat and mass flux. In addition, the effect of flow injection on the heat and mass transfer has also been considered. Governing parameters for the problem under study are the buoyancy ratio, N, and Lewis number, Le. Depending on the sign of the buoyancy ratio, inclusion of a concentration gradient may either assist or suppress the flow induced by thermal buoyancy. The Lewis number is found to have a more pronounced effect on the concentration field than it does on the flow and temperature fields. Results for Nusselt and Sherwood numbers cover a wide range of the governing parameters, −1

Natural Convection in A Vertical Porous Annulus

Natural convection in concentric, vertical annuli filled with saturated porous media is reviewed in this paper. Relevant works related to different thermal boundary conditions are discussed first, the attention being focused on analytical and numerical solutions for the Darcy flow model. Experimental investigations conducted by using various combinations of solid particles and fluids are discussed next. Finally, the results of a numerical investigation for a vertical annulus filled with spherical beads are presented. The Brinkman-Forchheimer-extended Darcy model is used as the momentum equation and the effect of porosity variation is taken into consideration. The predicted Nusselt numbers are compared with experimental results.

Non-Darcy mixed convection along a vertical wall in a saturated porous medium

In most of the previous studies of either natural or mixed convection, the boundary-layer formulation of Darcys law and the energy equation were used. However, the inertial effect is expected to become very significant when the pore Reynolds number is large. This is especially true for the case of either the high Rayleigh number regime or for high-porosity media. In spite of its importance in many applications, the non-Darcy flow effect has not received much attention. In this note, non-Darcy flow effects, which include the inertial and thermal dispersion effects, are closely examined. Steady-state non-Darcy convection, in the form of natural, mixed, and forced convection, is considered for a heated vertical surface embedded in a saturated porous medium.

Natural convection across a vertical layered porous cavity

Abstract Numerical studies are reported for steady-state natural convection in a two-dimensional layered porous cavity heated from the side wall. Emphasis is placed on the effects caused by the sublayer thickness ratio, permeability contrast and non-uniform conductivity in a system comprising two sublayers. Calculations have covered a wide range of these parameters. It has been observed that the flow and temperature fields for a layered structure with K1/K2 1. When the thermal properties are uniform, the average Nusselt number for a layered system of K1/K2 1, the average Nusselt number is always less than that of a homogeneous system, and it increases with both Rayleigh number and the thickness ratio. When there exists a difference in the thermal conductivity of the two sublayers, a second recirculating cell is generated in the less permeable layer for K1/K2 > 1. The average Nusselt number is found to increase with the conductivity ratio for K1/K2 > 1, and decrease for K1/K2 > 1. Heat transfer results including streamline and isotherm patterns, temperature and velocity profiles, and the Nusselt vs Rayleigh number relation in terms of these parameters, are presented.

FREE CONVECTION IN A VERTICAL ANNULUS WITH CONSTANT HEAT FLUX ON THE INNER WALL.

Heat transfer measurements are presented for free convection in a vertical annulus wherein the inner cylinder is at constant surface heat flux and the outer cylinder is at constant temperatuare. Overall heat transfer data re corrected for thermal radiation in the annulus. Rayleigh numbers span the conduction, transition and boundary layer regimes of flow, and average heat transfer coefficients are obtained with air and helium as the working fluids. The range of Rayleigh number is 10/sup 3/

Design of an Isotopic CT Scanner for Two Phase Flow Measurements

A feasibility study including parametric analysis, bubbly flow experimentation and preliminary hardware design has been completed for an isotopic CT scanner to interrogate two phase flows. The study results indicate a high speed fan beam scanner is feasible for measuring two phase flows under transient conditions by performing sequential scans. The major tradeoffs of this device compared to medical scanners are spatial resolution (1.15 cm), density resolution (3%), and source type (Cesium-137).

Aiding and opposing mixed convection in a vertical porous layer with a finite wall heat source

Two-dimensional, steady mixed convection in a vertical porous layer has been numerically studied for the case when a finite isothermal heat source is located on one vertical wall which is otherwise adiabatic and the other vertical wall is isothermally cooled. In the case of aiding mixed convection flow, the main flow separates from the cold wall and a recirculatory secondary flow exists in a region away from the heat source. However, when the main flow opposes buoyancy, the separation takes place on the heated wall, and the secondary flow is produced on the heated segment. Although the heat transfer rate increases with the aiding velocity, the effect is small at lower Peclet numbers (Pe). For the aiding flow, the slope of the Nusselt number curve increases with Peclet number unless the flow has approached the forced convection regime. For opposing flow, the heat transfer rate first decreases with an increase in Pe beyond zero and reaches a minimum before it starts increasing again. Under certain circumstances, the Nusselt number for a lower Rayleigh number may exceed that for a higher Ra.

Mixed Convection in Horizontal Porous Layers Heated From Below

Numerical studies are reported for steady, mixed convection in two-dimensional horizontal porous layer with localized heating from below. The interaction mechanism between the forced flow and the buoyant effects is examined for wide ranges of Rayleigh number Ra* and Peclet number Pe*. The external flow significantly perturbs the buoyancy-induced temperature and flow fields when Pe* is increased beyond unity. For a fixed Peclet number, an increase in Rayleigh number produces multicellular recirculating flows in a domain close to the heat source. This enhances heat transfer by free convection. However, for a fixed Ra*, an increase in forced flow or Peclet number does not necessarily increase the heat transfer rate. Hence, there exists a critical Peclet number as a function of Ra* for which the overall Nusselt number is minimum. The heat transfer is, generally, dominated by the buoyant flows for Pe* < 1 whereas the contribution of free convection is small for Pe* 10 when Ra* {le} 10.

A numerical investigation of thermal convection in a heat-generating fluid layer

Finite difference solutions of the equations governing thermal convection driven by uniform volumetric energy sources are presented for two-dimensional flows in a rectangular domain. The boundary conditions are a rigid (i.e, zero slip), zero heat-flux lower surface, rigid adiabatic sides, and either a rigid or free (i.e., zero shear) isothermal upper surface. Computations are carried out for Prandtl numbers from 0.05 to 20 and Rayleigh numbers from 5 x 10 to the 4th to 5 x 10 to the 8th. Nusselt numbers and average temperature profiles within the layer are in good agreement with experimental data for rigid-rigid boundaries. For rigid-free boundaries, Nusselt numbers are larger than in the former case. The structure of the flow and temperature fields in both cases is dominated by rolls, except at larger Rayleigh numbers where large-scale eddy transport occurs. Generally, low velocity upflows over broad regions of the layer are balanced by higher velocity downflows when the flow exhibits a cellular structure. The hydrodynamic constraint at the upper surface and the Prandtl number are found to influence only the detailed nature of flow and temperature fields. No truly steady velocity and temperature fields are found despite the fact that average Nusselt numbers reach steady values.